This frequency table shows the results of a small class quiz . If a student is selected at random, the probability that he or she scored 2, 4, or 5 is
`{:("Marks ", "Frequency "),(" "1," "4),(" "2," "3),(" "3," "2),(" "4," "6),(" "5," "5):}`

Options

A. `(3)/(20)`
B. `(1)/(4)`
C. `(7)/(10)`
D. `(9)/(20)`

Answer

To find the probability that a randomly selected student scored 2, 4, or 5 marks, we will follow these steps:

### Step 1: Calculate the total number of students
We need to sum the frequencies of all scores given in the frequency table.

- Frequency of students who scored 1: 4
- Frequency of students who scored 2: 3
- Frequency of students who scored 3: 2
- Frequency of students who scored 4: 6
- Frequency of students who scored 5: 5

Total number of students = 4 + 3 + 2 + 6 + 5

**Calculation:**
- 4 + 3 = 7
- 7 + 2 = 9
- 9 + 6 = 15
- 15 + 5 = 20

**Total number of students = 20**

### Step 2: Calculate the number of favorable outcomes
Next, we need to find out how many students scored either 2, 4, or 5 marks.

- Students who scored 2: 3
- Students who scored 4: 6
- Students who scored 5: 5

Total number of students who scored 2, 4, or 5 = 3 + 6 + 5

**Calculation:**
- 3 + 6 = 9
- 9 + 5 = 14

**Total number of favorable outcomes = 14**

### Step 3: Calculate the probability
The probability \( P \) that a student scored 2, 4, or 5 is given by the formula:

\[ P(\text{scoring 2, 4, or 5}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of students}} \]

Substituting the values we found:

\[ P(\text{scoring 2, 4, or 5}) = \frac{14}{20} \]

### Step 4: Simplify the fraction
Now we simplify the fraction \( \frac{14}{20} \).

Both the numerator and the denominator can be divided by 2:

\[ \frac{14 \div 2}{20 \div 2} = \frac{7}{10} \]

### Final Answer
The probability that a randomly selected student scored 2, 4, or 5 is \( \frac{7}{10} \).

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